New Symmetry Reductions, Dromions-Like and Compacton Solutions for a 2D BS ( m,n ) Equations Hierarchy with Fully Nonlinear Dispersion

O4; We have found two types of important exact solutions, compacton sohuttions, which are solitary waveswith the property that after colliding with their own kind, they re-emerge with the same coherent shape very much asthe solitons do during a completely elastic interaction, in the (1+1)D, (1+2)D and even (1+3)D models, and dromionsolutions (exponentially decaying solutions in all direction) in many (1+2)D and (1+3)D models. In this paper, symmetryreductions in (1+-2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m, n)equation) ut + b(um)xxy+ 4b(un uy)x = 0, which is a generalized model of (1+2)D break soliton equation ut +buxxy + 4buuy + 4bux-1uy = 0, by using the extended direct reduction method. As a result, six types of symmetryreductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitarywave solutions ofBS(l, n) equations, compacton solutions ofBS(m, m - 1) equations and the compacton-like solution ofthe potential form (called PBS(3, 2)) wxt + b(umx )xxy + 4b(wnxwy)x = 0. In addition, we show that the variable fx uy dxadmits dromion solutions rather than the field u itself in BS(1, n) equation.